讨论具有不同自变量的变系数模型的函数系数的估计及其大样本性质使用局部线性方法和积分方法，得到函数系数的积分估计由于该估计有较大的方差，进一步使用回切法改进这一估计，获得了函数系数的改进估计同时，研究了改进估计的渐近正态性最后，用模拟例子说明提出的估计方法是有效的。

半变系数模型已经获得了广泛的研究和应用，近几年，人们提出许多方法来估计其函数系数和常系数。在PLS方法基础上，本文给出半变系数模型模型在线性随机约束条件下的估计，并证明了常系数和函数系数估计的渐近正态性。

In this paper, we are concerned with statistical inference for the index parameter α0 in the single-index model Y=g (αT0X) + ε. Based on the estimates obtained by the local linear method, we extend the generalized likelihood ratio test to the single-index model. We investigate the asymptotic behaviour of the proposed test and demonstrate that its limiting null distribution follows a 2-distribution, with the scale constant and the number of degrees of freedom being independent of nuisance parameters or functions, which is called the Wilks phenomenon. A simulated example is used to illustrate the performance of the testing approach.

To perform hydrological forecasting, time series methods are often employed. In univariate time series, the autoregressive integrated moving average (ARIMA) model, the seasonal autoregressive moving average (SARMA) model, the deseasonalized model and the periodic autoregressive (PAR) model are often used. These models are based on the assumption that the influence of lagged riverflows on the riverflow is linear. In reality the assumption is often questionable. In this paper, the functional-coefficient autoregression (FCAR) model, which is a nonlinear model, is introduced to forecast riverflows. To explore the influence of the inflow on the outflow in a river system and to exploit the internal interaction of the outflows, bivariate time series models are needed. The transfer function (TF) model and the semi-parametric regression (SPR) model are often employed. In this paper, a new model, the non-parametric and functional-coefficient autoregression (NFCAR) model, is proposed. It consists of two parts: the first part, the non-parametric part explains the influences of the inflows on the outflow in a river system; the second part, the functional-coefficient linear part reveals the interactions among the outflows in a river system. By comparing the calibration and forecasting of the models, it is found that the NFCAR model performs very well.

This paper considers statistical inference for semiparametric varying coefficient partially linear models with error-prone linear covariates. An empirical likelihood based statistic for parametric component is developed to construct confidence regions. The resulting statistic is shown to be asymptotically chi-square distributed. By the empirical likelihood ratio function, the maximum empirical likelihood estimator of the parameter is defined and the asymptotic normality is shown. A simulation experiment is conducted to compare the empirical likelihood, normal based and the naive empirical likelihood methods in terms of coverage accuracies of confidence regions.

本文给出了样本相互独立，但不同分布的情况下后验概率函数的表达式及其与序贯后验概率函数之间的关系。在此基础上，给出了先验分布和条件分布为0-1分布情况下贝叶斯后验概率大小的比较方法，结合贝叶斯检验分析法安排医疗检查，使其在不降低诊断准确率的前提下，节省检查费用，提出了合理安排医疗检查的建议。

考虑部分线性单指标模型参数部分的统计推断问题。主要研究利用剖面最小二乘法（profile least-squares technique）估计模型的未知参数和函数，并利用该估计建立模型中参数部分的广义似然比（generalized likelihood ratio, GLR）检验统计量。在原假设条件下，文中新提出的GLR检验统计量渐近服从具有尺度常数（scale constant）与自由度独立于讨厌参数（nuisance parameters）的χ2-分布，这一现象被称为Wilks现象。最后给出数字模拟与实际例子，验证文中所提出的检验方法。

Varying coefficient error-in-covariables models are considered with surrogate data and validation sampling. Without specifying any error structure equation, two estimators for the coefficient function vector are suggested by using the local linear kernel smoothing technique. The proposed estimators are proved to be asymptotically normal. A bootstrap procedure is suggested to estimate the asymptotic variances. The data-driven bandwidth selection method is discussed. A simulation study is conducted to evaluate the proposed estimating methods.

To study the relationship between the levels of chemical pollutants and the number of daily total hospital admissions for respiratory diseases and to find the effect of temperature/relative humidity on the admission number, Wong et al. [17] introduced the varying-coefficient single-index model (VCSIM). As pointed out, it is a popular multivariate nonparametric fitting technique. However, the tests of the model have not been very well developed. In this paper, based on the estimators obtained by the local linear technique, the average method and the one-step back-fitting technique in the VCSIM, the generalized likelihood ratio (GLR) tests for varying-coefficient parts on the VCSIM are established. Under the null hypotheses the new proposed GLR tests follow the Â2-distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Simulations are conducted to evaluate the test procedure empirically. A real example is used to illustrate the performance of the testing approach.

Statistical inference on parametric part for the partially linear single-index model (PLSIM) is considered in this paper. A profile least-squares technique for estimating the parametric part is proposed and the asymptotic normality of the profile least-squares estimator is given. Based on the estimator, a generalized likelihood ratio (GLR) test is proposed to test whether parameters on linear part for the model is under a contain linear restricted condition. Under the null model, the proposed GLR statistic follows asymptotically the χ2-distribution with the scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Both simulated and real data examples are used to illustrate our proposed methods.